Which of these numbers is prime? ${15,\ 45,\ 47,\ 65,\ 66}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 15 are 1, 3, 5, and 15. The factors of 45 are 1, 3, 5, 9, 15, and 45. The factors of 47 are 1 and 47. The factors of 65 are 1, 5, 13, and 65. The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66. Thus, 47 is a prime number.